We study an encoding/decoding mechanism accounting for the relative spike timing of the signals propagating from peripheral nerve fibers to second-order somatosensory neurons in the cuneate nucleus (CN). The CN is modeled as a population of spiking neurons receiving as inputs the spatiotemporal responses of real mechanoreceptors obtained via microneurography recordings in humans. The efficiency of the haptic discrimination process is quantified by a novel definition of entropy that takes into full account the metrical properties of the spike train space. This measure proves to be a suitable decoding scheme for generalizing the classical Shannon entropy to spike-based neural codes. It permits an assessment of neurotransmission in the presence of a large output space (i.e. hundreds of spike trains) with 1 ms temporal precision. It is shown that the CN population code performs a complete discrimination of 81 distinct stimuli already within 35 ms of the first afferent spike, whereas a partial discrimination (80% of the maximum information transmission) is possible as rapidly as 15 ms. This study suggests that the CN may not constitute a mere synaptic relay along the somatosensory pathway but, rather, it may convey optimal contextual accounts (in terms of fast and reliable information transfer) of peripheral tactile inputs to downstream structures of the central nervous system.